This Exam P sample reference tests Conditional Probability. There are N known correct responses and one half of the remaining responses are correct on average. Solving N/[N+(20-N)/2]=0.824 gives N=14, choice C.
How to solve this Conditional Probability question
Setup
Setup
Among the 20 questions, the student answers the known questions correctly and guesses correctly on half of the remaining questions.
Pr(K∣C)=N+21(20−N)N=0.824
Model
Model
Conditional on a correct response, the probability that it came from the known set is the expected number of known correct responses divided by the expected total number of correct responses.
10+21NN≈0.824
Compute
Compute
Solving the resulting equation gives 14. Substitution gives fourteen seventeenths, approximately 0.824, confirming the required rounding.
N=14,14+314=0.823529≈0.824
Answer
Answer
The student knows 14 of the answers.
14(C)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
ASubstituting 8 known answers gives a conditional probability of about 0.571, not 0.824.
BSubstituting 10 known answers gives a conditional probability of about 0.667, not 0.824.
DSubstituting 16 known answers gives a conditional probability of about 0.889, not 0.824.
ESubstituting 18 known answers gives a conditional probability of about 0.947, not 0.824.
Original practice · fully worked
Original variant: known answers on a four-choice quiz
A learner answers a 30-question multiple-choice quiz. The learner knows N answers and guesses independently among four choices on all remaining questions. Given a correct response, the probability it was known is 0.80. Find N.
A 10
B 12
C 15
D 18
E 20
Variant answer in brief
Known answers contribute N correct responses and guesses contribute (30-N)/4. Setting the known share equal to 0.80 gives N=15, choice C.
Setup
Setup
The learner answers all known questions correctly and guesses correctly on one quarter of the remaining questions.
N+41(30−N)N=0.80
Model
Model
Given that a response is correct, compare the number of known correct responses with the total expected number of correct responses.
N=0.80(43N+7.5)
Compute
Compute
Solving the conditional-probability equation gives 15 known answers.
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
